Rotational Alignment Decay and Decoherence of Molecular Superrotors

We present the quantum master equation describing the coherent and incoherent dynamics of a rapidly rotating molecule in the presence of a thermal background gas. The master equation relates the rate of rotational alignment decay and decoherence to the microscopic scattering amplitudes, which we calculate for anisotropic van der Waals scattering. For large rotational energies, we find quantitative agreement of the resulting alignment decay rate with recent superrotor experiments.

Figure 1

A rapidly rotating linear molecule (blue) embedded in a homogeneous thermal gas (red) of density $n_g$ and temperature $T$ experiences collisions with environmental gas particles. If the molecule rotates multiple times during the collision, as in the case of superrotors, the interaction with the gas leads to rotational decoherence as well as reorientation of the mean angular momentum $⟨\mathsf{J}⟩$. The rotor of orientation $\mathbf{m}$ interacts via the attractive van der Waals interaction [Eq. (4)] with a gas particle at distance $r$, which impinges with relative momentum $q{\mathbf{n}}^{\prime }$ and leaves with relative momentum $q\mathbf{n}$.

Figure 2

In the superrotor regime, characterized by the absence of inelastic collisions, the theoretically predicted decay of rotational coherences (black solid line) compares very well with the experimental data (black diamonds) taken from Ref. [10]. The theoretical rate [Eq. (5)] includes no free parameters but is based on the microscopic scattering amplitudes of individual superrotor–gas particle collisions. For the considered nitrogen molecules, the superrotor regime starts at $j\simeq 50$, as can be seen from the fraction of $j$-conserving collisions (blue squares, right axis) approaching unity. The elastic fraction is obtained by numerically calculating the total scattering cross sections (using Molscat [40]) for atom-linear-rotor scattering with a Lennard-Jones potential exhibiting the orientation dependence of Eq. (4). The molecular polarizabilities are taken from Ref. [41], and the $C_6$ constant is from the Lennard-Jones parameters listed in Ref. [42].